%\documentclass[12pt]{article} %\usepackage{showkeys,amssymb} %\usepackage{mltex} \usepackage[frenchb]{babel} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{amssymb} \usepackage{times} \pagestyle{empty} \topmargin= -1,5cm \textwidth= 17,5cm\textheight= 25cm\oddsidemargin=-1,05cm \newcommand{\ba}{\begin{array}} \newcommand{\ea}{\end{array}} \newcommand{\bc}{\begin{center}} \newcommand{\ec}{\end{center}} \newcommand{\be}{\begin{enumerate}} \newcommand{\ee}{\end{enumerate}} \newcommand{\beq}{\begin{eqnarray}} \newcommand{\eeq}{\end{eqnarray}} \newcommand{\beQ}{\begin{eqnarray*}} \newcommand{\eeQ}{\end{eqnarray*}} \newcommand{\bi}{\begin{itemize}} \newcommand{\ei}{\end{itemize}} \newcommand{\bt}{\begin{tabular}} \newcommand{\et}{\end{tabular}} \newcommand{\bdm}{\begin{displaymath}} \newcommand{\edm}{\end{displaymath}} \newcommand{\vect}{\overrightarrow} \newcommand{\lrw}{\longrightarrow} \newcommand{\Lrw}{\Longrightarrow} \newcommand{\Llrw}{\Longleftrightarrow} \newcommand{\ds}{\displaystyle} \newcommand{\lv}{\left\vert} \newcommand{\rv}{\right\vert} \newcommand{\llv}{\lv\lv} \newcommand{\rrv}{\rv\rv} \newcommand{\ve}{\varepsilon} \newcommand{\vf}{\varphi} \newcommand{\im}{\imath} %\newcommand{\r}{{\bf R}} %\newcommand{\C}{{\bf C}} %\newcommand{\cc}{{\cal C}} \newcommand{\cl}{{\cal L}} \let\pa=\partial \newcommand{\vz}{\vert z \vert} %\newcommand{\sn1}{\sum_{n=1}^{\infty}\;} %\newcommand{\s0}{\sum_{n=0}^{\infty} \;} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%Styles%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \let\B=\mathbb \let\Bbb=\mathbb \let\cal=\mathcal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%Lettres Grecques%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \let\a=\alpha %\let\A= \let\b=\beta %\let\B=\mathbb \let\c=\chi %\let\C=\mathcal \let\d=\delta \let\D=\Delta \let\e=\varepsilon \let\eps=\epsilon %\let\E= %\let\f=\varphi \let\F=\Phi \let\g=\gamma \let\G=\Gamma \let\h=\ell %\let\H= \let\i=\iota %\let\I= %\let\j= %\def\J \let\k=\kappa %\let\K= \let\l=\lambda \let\L=\Lambda \let\m=\mu \let\M=\Mu \let\nu=\nu % \n est une macro de diagram.tex \let\N=\nabla \let\p=\pi \let\P=\Pi %\let\q= %\let\Q= \let\r=\rho %\let\R= \let\s=\sigma \let\S=\Sigma \let\t=\tau %\let\T= \let\u=\theta \let\U=\Theta %\let\v= %\let\V= \let\w=\omega \let\W=\Omega \let\x=\xi \let\X=\Xi \let\y=\psi \let\Y=\Psi \let\z=\zeta %\let\Z= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%\mathbb%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\bC{{\mathbb C}} \def\bD{{\mathbb D}} \def\bF{{\mathbb F}} \def\bH{{\mathbb H}} \def\bI{{\mathbb I}} \def\bK{{\mathbb K}} \def\bbN{{\mathbb N}} \def\bQ{{\mathbb Q}} \def\bR{{\mathbb R}} \def\bT{{\mathbb T}} \def\bV{{\mathbb V}} \def\bW{{\mathbb W}} \def\bZ{{\mathbb Z}} \def\ebC{\bC\setminus \{0\}} \def\ebN{\bbN\setminus \{0\}} \def\ebZ{\bZ\setminus \{0\}} \def\ebR{\bR\setminus \{0\}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%\mathcal%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\cA{\mathcal A} \def\cB{\mathcal B} \def\cC{\mathcal C} \def\cD{\mathcal D} \def\cE{\mathcal E} \def\cF{\mathcal F} \def\cG{\mathcal G} \def\cH{\mathcal H} \def\cI{\mathcal I} \def\cJ{\mathcal J} \def\cK{\mathcal K} \def\cL{\mathcal L} \def\cM{\mathcal M} \def\cN{\mathcal N} \def\cO{\mathcal O} \def\cP{\mathcal P} \def\cQ{\mathcal Q} \def\cR{\mathcal R} \def\cS{\mathcal S} \def\cT{\mathcal T} \def\cU{\mathcal U} \def\cV{\mathcal V} \def\cW{\mathcal W} \def\cX{\mathcal X} \def\cY{\mathcal Y} \def\cZ{\mathcal Z} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%\mathfrak%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\ga{\mathfrak{a}} \def\gg{\mathfrak{g}} \def\gh{\mathfrak{h}} \def\gk{\mathfrak{k}} \def\gl{\mathfrak{l}} \def\gm{\mathfrak{m}} \def\gn{\mathfrak{n}} \def\gp{\mathfrak{p}} \def\gq{\mathfrak{q}} \def\gs{\mathfrak{s}} \def\gt{\mathfrak{t}} \def\gU{\mathfrak{U}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%Raccourcis de texte%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\ni{\noindent} \let\nl=\newline \def\ss{\smallskip} \def\ms{\medskip} \def\bs{\bigskip} \def\qed{\rightline{Q.E.D.}\ss} \def\td{\tilde} \def\ath{a^{ \underline{\textstyle{th}}}} \def\ith{i^{\underline{\textstyle{th}}}} %math% \def\ci{C^\infty} \def\midp{\,:\,} \def\op{{\scriptstyle\circ}} \def\ddt{{{d}\over{dt}}} %op{\`E}rations% \let\bar=\overline \let\bop=\bigoplus \let\cd=\cdot \let\ld=\ldots \let\os=\oplus \let\ot=\otimes %fl{\"E}ches% \let\da=\downarrow \let\la=\leftarrow \let\lra=\leftrightarrow \let\Lra=\Leftrightarrow \let\ra=\rightarrow \let\ua=\uparrow %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%Operateurs%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\ad{{\rm{ad}}} \def\Ad{{\rm{Ad}}} \def\Alt{{\rm{Alt}}} \def\auto{{\rm {Aut}}} \def\cas{{\rm {Cas}}} \def\diff{{\rm {Diff}}} \def\diffeo{{\rm {Diffeo}}} \def\endo{{\rm {End}}} \def\grad{{\rm {grad}}} \def\hess{{\rm {Hess}}} \def\hom{{\rm {Hom}}} \def\id{{\rm {Id}}} \def\Ind{\rm {Ind}} \def\inf{\rm {inf}} \def\irr{\rm {Irr}} \def\ker{{\rm {ker}}} \def\coker{{\rm {coker}}} \def\op{{\scriptstyle{\circ}}} \def\proj{{\rm {Proj}}} \def\re{{\rm {Re}}} \def\res{{\textrm {R{\'e}s}}} \def\sgn{{\rm {sgn}}} \def\spa{{\rm {span}}} \def\sup{{\rm {sup}}} \def\supp{{\rm {supp}}} \def\symm{{\rm {Symm}}} \def\tr{{\rm {tr}}} \def\Tr{{\rm {Tr}}} \def\area{{\rm {area}}} \def\vol{{\rm {vol}}} \newcommand{\lto}{\ensuremath{\longrightarrow}} \newcommand{\function}[5] {\beQ\begin{array}{r@{}ccl} #1 \colon\; & #2 &\lto & #3 \\[.05cm] & #4 &\longmapsto & #5 \end{array}\eeQ} %\function {f}{\R^n}{Cl^0_{n+1}}{e_i}{ e_i\cdot e_{n+1}.} %%%%%%%%ajout par Koziarz %\textwidth= 17,5cm \oddsidemargin=-7mm %\input{option_keys} %\usepackage[frenchb]{babel} %\usepackage{amssymb} %\usepackage{times} %\parindent0em %\pagestyle{empty} \newcommand{\nc}{\newcommand} %\nc{\op}[1]{\mathop{\mathsf{#1}}\nolimits} \nc{\aeq}{\begin{equation}}\nc{\zeq}{\end{equation}} %\nc{\mb}{\mathbb} %\nc{\mc}{\mathcal} \nc{\bb}{\bigskip} \nc{\cl}{\centerline} \nc{\ind}{\hskip 1em\relax} \def\R{{\mathbb R}} \def\C{{\mathbb C}} \def\N{{\mathbb N}} \begin{document} \hskip-1,3mm {\large\bf Universit{\'e} Henri Poincar{\'e}\hfill Faculté des Sciences et Techniques} \hskip-1,3mm {\sl Calculs et Mathématiques\hfill } \hskip-1,3mm {\sl { \hfill Ann{\'e}e 2010/2011}}